(%i1) batch(diffeq.max)
read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max
(%i2) load(stringproc)
(%o2) /usr/local/share/maxima/5.26.0/share/contrib/stringproc/stringproc.mac
(%i3) reached_interval() := block([ret],
if (((array_x >= glob_next_display) and (not glob_neg_h))
1
or ((array_x <= glob_next_display) and glob_neg_h))
1
or (glob_next_display = 0.0) then ret : true else ret : false, return(ret))
(%o3) reached_interval() := block([ret],
if (((array_x >= glob_next_display) and (not glob_neg_h))
1
or ((array_x <= glob_next_display) and glob_neg_h))
1
or (glob_next_display = 0.0) then ret : true else ret : false, return(ret))
(%i4) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
relerr
if relerr # 0.0 then glob_good_digits : - floor(log10(------))
100.0
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%o4) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
relerr
if relerr # 0.0 then glob_good_digits : - floor(log10(------))
100.0
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%i5) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%o5) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%i6) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), percent_done :
comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%o6) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), percent_done :
comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%i7) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1,
nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found], n : glob_max_terms,
m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float)) do m :
1, m - 2
array_y_higher
1, m
m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m - 1) rm0
array_y_higher
1, m - 2
- convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
elseif (omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 5
then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (array_complex_pole :
1, 1
glob_large_float, array_complex_pole : glob_large_float)
1, 2
else (if omniabs(nr1 dr2 - nr2 dr1) > glob_small_float
dr1 dr2 - ds2 dr1 + ds1 dr2
then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found : false, if (not found) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS,
"Complex estimate of poles used")), if (not found)
and ((array_real_pole # glob_large_float) and (array_real_pole # glob_large_float)
1, 1 1, 2
and (array_real_pole > 0.0) and (array_real_pole > 0.0)
1, 1 1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0)))
1, 1 1, 2 1, 1 1, 2
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found : true, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS,
"Complex estimate of poles used")), if not found
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float,
1
array_pole : glob_large_float, if array_pole > array_poles
2 1 1, 1
then (array_pole : array_poles , array_pole : array_poles ),
1 1, 1 2 1, 2
if reached_interval() then display_pole())
(%o7) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1,
nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found], n : glob_max_terms,
m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float)) do m :
1, m - 2
array_y_higher
1, m
m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m - 1) rm0
array_y_higher
1, m - 2
- convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
elseif (omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 5
then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (array_complex_pole :
1, 1
glob_large_float, array_complex_pole : glob_large_float)
1, 2
else (if omniabs(nr1 dr2 - nr2 dr1) > glob_small_float
dr1 dr2 - ds2 dr1 + ds1 dr2
then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found : false, if (not found) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS,
"Complex estimate of poles used")), if (not found)
and ((array_real_pole # glob_large_float) and (array_real_pole # glob_large_float)
1, 1 1, 2
and (array_real_pole > 0.0) and (array_real_pole > 0.0)
1, 1 1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0)))
1, 1 1, 2 1, 1 1, 2
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found : true, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS,
"Complex estimate of poles used")), if not found
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float,
1
array_pole : glob_large_float, if array_pole > array_poles
2 1 1, 1
then (array_pole : array_poles , array_pole : array_poles ),
1 1, 1 2 1, 2
if reached_interval() then display_pole())
(%i8) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%o8) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%i9) atomall() := block([kkk, order_d, adj2, temporary, term, temp, temp2],
array_tmp1 : array_x array_x , array_tmp2 : array_tmp1 + array_const_0D0 ,
1 1 1 1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 2,
glob_h 2, 1
array_tmp1 : array_x array_x + array_x array_x ,
2 2 1 1 2
array_tmp2 : array_tmp1 , if not array_y_set_initial
2 2 1, 3
then (if 2 <= glob_max_terms then (temporary :
array_tmp2 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary,
2 3
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 3 glob_h
array_y_higher : temporary)), kkk : 3, array_tmp1 : array_x array_x ,
2, 2 3 2 2
array_tmp2 : array_tmp1 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
array_tmp2 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary,
3 4
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y_higher : temporary)), kkk : 4, array_tmp2 : array_tmp1 ,
2, 3 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 5,
glob_h 2, 4
array_tmp2 : array_tmp1 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
array_tmp2 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary,
5 6
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y_higher : temporary)), kkk : 6,
2, 5
while kkk <= glob_max_terms do (array_tmp2 : array_tmp1 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
array_tmp2 expt(glob_h, order_d)
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_y : temporary, array_y_higher : temporary,
order_d + kkk 1, order_d + kkk
term : - 1 + order_d + kkk, adj2 : 2, while (adj2 <= 1 + order_d)
temporary convfp(adj2)
and (term >= 1) do (temporary : ----------------------,
glob_h
array_y_higher : temporary, adj2 : 1 + adj2, term : term - 1))),
adj2, term
kkk : 1 + kkk))
(%o9) atomall() := block([kkk, order_d, adj2, temporary, term, temp, temp2],
array_tmp1 : array_x array_x , array_tmp2 : array_tmp1 + array_const_0D0 ,
1 1 1 1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 2,
glob_h 2, 1
array_tmp1 : array_x array_x + array_x array_x ,
2 2 1 1 2
array_tmp2 : array_tmp1 , if not array_y_set_initial
2 2 1, 3
then (if 2 <= glob_max_terms then (temporary :
array_tmp2 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary,
2 3
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 3 glob_h
array_y_higher : temporary)), kkk : 3, array_tmp1 : array_x array_x ,
2, 2 3 2 2
array_tmp2 : array_tmp1 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
array_tmp2 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary,
3 4
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y_higher : temporary)), kkk : 4, array_tmp2 : array_tmp1 ,
2, 3 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 5,
glob_h 2, 4
array_tmp2 : array_tmp1 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
array_tmp2 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary,
5 6
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y_higher : temporary)), kkk : 6,
2, 5
while kkk <= glob_max_terms do (array_tmp2 : array_tmp1 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
array_tmp2 expt(glob_h, order_d)
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_y : temporary, array_y_higher : temporary,
order_d + kkk 1, order_d + kkk
term : - 1 + order_d + kkk, adj2 : 2, while (adj2 <= 1 + order_d)
temporary convfp(adj2)
and (term >= 1) do (temporary : ----------------------,
glob_h
array_y_higher : temporary, adj2 : 1 + adj2, term : term - 1))),
adj2, term
kkk : 1 + kkk))
log(x)
(%i10) log10(x) := ---------
log(10.0)
log(x)
(%o10) log10(x) := ---------
log(10.0)
(%i11) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%o11) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%i12) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%o12) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%i13) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%o13) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%i14) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%o14) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%i15) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%o15) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%i16) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%o16) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%i17) dump_series(iolevel, dump_label, series_name, array_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%o17) dump_series(iolevel, dump_label, series_name, array_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%i18) dump_series_2(iolevel, dump_label, series_name, array_series2, numb,
subnum) := block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%o18) dump_series_2(iolevel, dump_label, series_name, array_series2, numb,
subnum) := block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%i19) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%o19) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%i20) logitem_time(fd, secs_in) := block([cent_int, centuries, days,
days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int,
sec_in_millinium, sec_int, seconds, secs, years, years_int], secs : secs_in,
printf(fd, "
"), if secs >= 0.0 then (sec_in_millinium :
sec_in_minute min_in_hour hours_in_day days_in_year years_in_century
secs
centuries_in_millinium, milliniums : ----------------,
sec_in_millinium
millinium_int : floor(milliniums), centuries :
(milliniums - millinium_int) centuries_in_millinium,
cent_int : floor(centuries), years : (centuries - cent_int) years_in_century,
years_int : floor(years), days : (years - years_int) days_in_year,
days_int : floor(days), hours : (days - days_int) hours_in_day,
hours_int : floor(hours), minutes : (hours - hours_int) min_in_hour,
minutes_int : floor(minutes), seconds : (minutes - minutes_int) sec_in_minute,
sec_int : floor(seconds), if millinium_int > 0 then printf(fd, "~d Millinia ~d\
Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elseif cent_int > 0 then printf(fd,
"~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", cent_int,
years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0
then printf(fd, "~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "~d Days ~d Hours ~d Minutes ~d Seconds", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "~d Hours ~d Minutes ~d Seconds", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "~d Minutes ~d Seconds",
minutes_int, sec_int) else printf(fd, "~d Seconds", sec_int))
else printf(fd, "Unknown"), printf(fd, " | "))
(%o20) logitem_time(fd, secs_in) := block([cent_int, centuries, days,
days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int,
sec_in_millinium, sec_int, seconds, secs, years, years_int], secs : secs_in,
printf(fd, ""), if secs >= 0.0 then (sec_in_millinium :
sec_in_minute min_in_hour hours_in_day days_in_year years_in_century
secs
centuries_in_millinium, milliniums : ----------------,
sec_in_millinium
millinium_int : floor(milliniums), centuries :
(milliniums - millinium_int) centuries_in_millinium,
cent_int : floor(centuries), years : (centuries - cent_int) years_in_century,
years_int : floor(years), days : (years - years_int) days_in_year,
days_int : floor(days), hours : (days - days_int) hours_in_day,
hours_int : floor(hours), minutes : (hours - hours_int) min_in_hour,
minutes_int : floor(minutes), seconds : (minutes - minutes_int) sec_in_minute,
sec_int : floor(seconds), if millinium_int > 0 then printf(fd, "~d Millinia ~d\
Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elseif cent_int > 0 then printf(fd,
"~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", cent_int,
years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0
then printf(fd, "~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "~d Days ~d Hours ~d Minutes ~d Seconds", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "~d Hours ~d Minutes ~d Seconds", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "~d Minutes ~d Seconds",
minutes_int, sec_int) else printf(fd, "~d Seconds", sec_int))
else printf(fd, "Unknown"), printf(fd, " | "))
(%i21) omniout_timestr(secs_in) := block([cent_int, centuries, days, days_int,
hours, hours_int, millinium_int, milliniums, minutes, minutes_int,
sec_in_millinium, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= convfloat(0.0)
then (sec_in_millinium : convfloat(sec_in_minute) convfloat(min_in_hour)
convfloat(hours_in_day) convfloat(days_in_year) convfloat(years_in_century)
secs
convfloat(centuries_in_millinium), milliniums : ---------------------------,
convfloat(sec_in_millinium)
millinium_int : floor(milliniums), centuries :
(milliniums - millinium_int) convfloat(centuries_in_millinium),
cent_int : floor(centuries), years : (centuries - cent_int)
convfloat(years_in_century), years_int : floor(years),
days : (years - years_int) convfloat(days_in_year), days_int : floor(days),
hours : (days - days_int) convfloat(hours_in_day), hours_int : floor(hours),
minutes : (hours - hours_int) convfloat(min_in_hour),
minutes_int : floor(minutes), seconds :
(minutes - minutes_int) convfloat(sec_in_minute), sec_int : floor(seconds),
if millinium_int > 0 then printf(true,
"= ~d Millinia ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%",
millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elseif cent_int > 0 then printf(true,
"= ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", cent_int,
years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0
then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%",
years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%o21) omniout_timestr(secs_in) := block([cent_int, centuries, days, days_int,
hours, hours_int, millinium_int, milliniums, minutes, minutes_int,
sec_in_millinium, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= convfloat(0.0)
then (sec_in_millinium : convfloat(sec_in_minute) convfloat(min_in_hour)
convfloat(hours_in_day) convfloat(days_in_year) convfloat(years_in_century)
secs
convfloat(centuries_in_millinium), milliniums : ---------------------------,
convfloat(sec_in_millinium)
millinium_int : floor(milliniums), centuries :
(milliniums - millinium_int) convfloat(centuries_in_millinium),
cent_int : floor(centuries), years : (centuries - cent_int)
convfloat(years_in_century), years_int : floor(years),
days : (years - years_int) convfloat(days_in_year), days_int : floor(days),
hours : (days - days_int) convfloat(hours_in_day), hours_int : floor(hours),
minutes : (hours - hours_int) convfloat(min_in_hour),
minutes_int : floor(minutes), seconds :
(minutes - minutes_int) convfloat(sec_in_minute), sec_int : floor(seconds),
if millinium_int > 0 then printf(true,
"= ~d Millinia ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%",
millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elseif cent_int > 0 then printf(true,
"= ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", cent_int,
years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0
then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%",
years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%i22) ats(mmm_ats, array_a, array_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : array_a array_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%o22) ats(mmm_ats, array_a, array_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : array_a array_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%i23) att(mmm_att, array_aa, array_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : array_aa array_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%o23) att(mmm_att, array_aa, array_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : array_aa array_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%i24) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%o24) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%i25) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%o25) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%i26) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%o26) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%i27) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%o27) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%i28) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error # 0.0
rel_error
then (good_digits : - floor(log10(---------)),
100.0
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%o28) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error # 0.0
rel_error
then (good_digits : - floor(log10(---------)),
100.0
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%i29) log_revs(file, revs) := printf(file, revs)
(%o29) log_revs(file, revs) := printf(file, revs)
(%i30) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%o30) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%i31) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%o31) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%i32) logstart(file) := printf(file, "")
(%o32) logstart(file) := printf(file, "
")
(%i33) logend(file) := printf(file, "
~%")
(%o33) logend(file) := printf(file, "~%")
(%i34) not_reached_end(x, x_end) := block([ret],
if (glob_neg_h and (x > x_end)) or ((not glob_neg_h) and (x < x_end))
then ret : true else ret : false, ret)
(%o34) not_reached_end(x, x_end) := block([ret],
if (glob_neg_h and (x > x_end)) or ((not glob_neg_h) and (x < x_end))
then ret : true else ret : false, ret)
(%i35) chk_data() := block([errflag], errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%o35) chk_data() := block([errflag], errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%i36) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) :=
block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2,
sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%o36) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) :=
block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2,
sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%i37) comp_percent(t_end2, t_start2, t2) :=
block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%o37) comp_percent(t_end2, t_start2, t2) :=
block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%i38) factorial_2(nnn) := block([ret], ret : nnn!)
(%o38) factorial_2(nnn) := block([ret], ret : nnn!)
(%i39) factorial_1(nnn) := block([ret],
if nnn <= glob_max_terms then (if array_fact_1 = 0
nnn
then (ret : factorial_2(nnn), array_fact_1 : ret)
nnn
else ret : array_fact_1 ) else ret : factorial_2(nnn), ret)
nnn
(%o39) factorial_1(nnn) := block([ret],
if nnn <= glob_max_terms then (if array_fact_1 = 0
nnn
then (ret : factorial_2(nnn), array_fact_1 : ret)
nnn
else ret : array_fact_1 ) else ret : factorial_2(nnn), ret)
nnn
(%i40) factorial_3(mmm, nnn) := block([ret],
if (nnn <= glob_max_terms) and (mmm <= glob_max_terms)
factorial_1(mmm)
then (if array_fact_2 = 0 then (ret : ----------------,
mmm, nnn factorial_1(nnn)
array_fact_2 : ret) else ret : array_fact_2 )
mmm, nnn mmm, nnn
factorial_2(mmm)
else ret : ----------------, ret)
factorial_2(nnn)
(%o40) factorial_3(mmm, nnn) := block([ret],
if (nnn <= glob_max_terms) and (mmm <= glob_max_terms)
factorial_1(mmm)
then (if array_fact_2 = 0 then (ret : ----------------,
mmm, nnn factorial_1(nnn)
array_fact_2 : ret) else ret : array_fact_2 )
mmm, nnn mmm, nnn
factorial_2(mmm)
else ret : ----------------, ret)
factorial_2(nnn)
(%i41) convfp(mmm) := mmm
(%o41) convfp(mmm) := mmm
(%i42) convfloat(mmm) := mmm
(%o42) convfloat(mmm) := mmm
(%i43) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%o43) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%i44) arcsin(x) := asin(x)
(%o44) arcsin(x) := asin(x)
(%i45) arccos(x) := acos(x)
(%o45) arccos(x) := acos(x)
(%i46) arctan(x) := atan(x)
(%o46) arctan(x) := atan(x)
(%i47) omniabs(x) := abs(x)
(%o47) omniabs(x) := abs(x)
y
(%i48) expt(x, y) := x
y
(%o48) expt(x, y) := x
x x x
(%i49) exact_soln_y(x) := ----- + 1.0
3.0
x x x
(%o49) exact_soln_y(x) := ----- + 1.0
3.0
(%i50) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord,
order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter,
calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm,
max_terms, opt_iter, tmp, subiter], define_variable(INFO, 2, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(glob_iolevel, 5, fixnum),
define_variable(glob_max_terms, 30, fixnum),
define_variable(ALWAYS, 1, fixnum), define_variable(glob_max_sec, 10000.0,
float), define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_initial_pass, true, boolean),
define_variable(min_in_hour, 60, fixnum),
define_variable(djd_debug2, true, boolean),
define_variable(glob_dump, false, boolean),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_display_interval, 0.0, float),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_almost_1, 0.999, float),
define_variable(djd_debug, true, boolean),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_disp_incr, 0.1, float),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_hmax, 1.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_log10normmin, 0.1, float),
define_variable(years_in_century, 100, fixnum),
define_variable(days_in_year, 365, fixnum),
define_variable(hours_in_day, 24, fixnum),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_warned2, false, boolean),
define_variable(glob_warned, false, boolean),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_next_display, 0.0, float),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_h, 0.1, float), define_variable(glob_optimal_done, false,
boolean), define_variable(centuries_in_millinium, 10, fixnum),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_neg_h, false, boolean),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(sec_in_minute, 60, fixnum),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_percent_done, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS, "##############temp/multpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = x * x ;"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "Digits : 32,"), omniout_str(ALWAYS, "max_terms : 30,"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start : 0.1,"), omniout_str(ALWAYS, "x_end : 10.0 ,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h : 0.00001 ,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 20,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_h : 0.005 ,"),
omniout_str(ALWAYS, "glob_display_interval : 0.1,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 10000,"),
omniout_str(ALWAYS, "glob_max_minutes : 10,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := ("),
omniout_str(ALWAYS, " (1.0 + x * x * x / 3.0) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_type_pole, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_y_init, 1 + max_terms), array(array_last_rel_error,
1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y_higher_work, 1 + 2,
1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms), term : 1,
while term <= max_terms do (array_type_pole : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_y_init : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_last_rel_error : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_pole : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1,
term
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_real_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_const_0D0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1,
iiif, jjjf
x_end : 10.0, array_y_init : exact_soln_y(x_start), glob_h : 1.0E-5,
1 + 0
glob_look_poles : true, glob_max_iter : 20, glob_h : 0.005,
glob_display_interval : 0.1, glob_look_poles : true, glob_max_iter : 10000,
glob_max_minutes : 10, glob_last_good_h : glob_h, glob_max_terms : max_terms,
glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_abserr : expt(10.0, glob_log10_abserr),
glob_relerr : expt(10.0, glob_log10_relerr),
if glob_h > 0.0 then (glob_neg_h : false,
glob_display_interval : omniabs(glob_display_interval))
else (glob_neg_h : true, glob_display_interval :
- omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true,
1, 1
array_y_set_initial : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, array_y_set_initial : false,
1, 20 1, 21
array_y_set_initial : false, array_y_set_initial : false,
1, 22 1, 23
array_y_set_initial : false, array_y_set_initial : false,
1, 24 1, 25
array_y_set_initial : false, array_y_set_initial : false,
1, 26 1, 27
array_y_set_initial : false, array_y_set_initial : false,
1, 28 1, 29
array_y_set_initial : false, if glob_html_log
1, 30
then html_log_file : openw("html/entry.html"),
omniout_str(ALWAYS, "START of Soultion"), array_x : x_start,
1
array_x : glob_h, glob_next_display : x_start, order_diff : 1, term_no : 1,
2
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(),
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp),
1, 1
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "),
glob_reached_optimal_h : true, glob_optimal_clock_start_sec :
elapsed_time_seconds(), while (glob_current_iter < glob_max_iter)
and not_reached_end(array_x , x_end) and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
1
convfloat(glob_max_sec)) do (if reached_interval
() then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter, atomall(),
if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 1, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1),
ord, term_no
display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"),
if glob_iter >= glob_max_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(),
omniout_str(INFO, "diff ( y , x , 1 ) = x * x ;"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2012-09-21T03:05:28-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "mult"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = x * x ;"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_optimal_expect_sec)), 0)
else (logitem_str(html_log_file, "Done"), 0),
log_revs(html_log_file, " 130 | "), logitem_str(html_log_file, "mult diffeq.max"), logitem_str(html_log_file, "mult maxima results"),
logitem_str(html_log_file, "c c++ Maple and Maxima"), logend(html_log_file)),
if glob_html_log then close(html_log_file))
(%o50) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord,
order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter,
calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm,
max_terms, opt_iter, tmp, subiter], define_variable(INFO, 2, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(glob_iolevel, 5, fixnum),
define_variable(glob_max_terms, 30, fixnum),
define_variable(ALWAYS, 1, fixnum), define_variable(glob_max_sec, 10000.0,
float), define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_initial_pass, true, boolean),
define_variable(min_in_hour, 60, fixnum),
define_variable(djd_debug2, true, boolean),
define_variable(glob_dump, false, boolean),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_display_interval, 0.0, float),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_almost_1, 0.999, float),
define_variable(djd_debug, true, boolean),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_disp_incr, 0.1, float),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_hmax, 1.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_log10normmin, 0.1, float),
define_variable(years_in_century, 100, fixnum),
define_variable(days_in_year, 365, fixnum),
define_variable(hours_in_day, 24, fixnum),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_warned2, false, boolean),
define_variable(glob_warned, false, boolean),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_next_display, 0.0, float),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_h, 0.1, float), define_variable(glob_optimal_done, false,
boolean), define_variable(centuries_in_millinium, 10, fixnum),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_neg_h, false, boolean),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(sec_in_minute, 60, fixnum),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_percent_done, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS, "##############temp/multpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = x * x ;"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "Digits : 32,"), omniout_str(ALWAYS, "max_terms : 30,"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start : 0.1,"), omniout_str(ALWAYS, "x_end : 10.0 ,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h : 0.00001 ,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 20,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_h : 0.005 ,"),
omniout_str(ALWAYS, "glob_display_interval : 0.1,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 10000,"),
omniout_str(ALWAYS, "glob_max_minutes : 10,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := ("),
omniout_str(ALWAYS, " (1.0 + x * x * x / 3.0) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_type_pole, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_y_init, 1 + max_terms), array(array_last_rel_error,
1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y_higher_work, 1 + 2,
1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms), term : 1,
while term <= max_terms do (array_type_pole : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_y_init : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_last_rel_error : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_pole : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1,
term
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_real_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_const_0D0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1,
iiif, jjjf
x_end : 10.0, array_y_init : exact_soln_y(x_start), glob_h : 1.0E-5,
1 + 0
glob_look_poles : true, glob_max_iter : 20, glob_h : 0.005,
glob_display_interval : 0.1, glob_look_poles : true, glob_max_iter : 10000,
glob_max_minutes : 10, glob_last_good_h : glob_h, glob_max_terms : max_terms,
glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_abserr : expt(10.0, glob_log10_abserr),
glob_relerr : expt(10.0, glob_log10_relerr),
if glob_h > 0.0 then (glob_neg_h : false,
glob_display_interval : omniabs(glob_display_interval))
else (glob_neg_h : true, glob_display_interval :
- omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true,
1, 1
array_y_set_initial : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, array_y_set_initial : false,
1, 20 1, 21
array_y_set_initial : false, array_y_set_initial : false,
1, 22 1, 23
array_y_set_initial : false, array_y_set_initial : false,
1, 24 1, 25
array_y_set_initial : false, array_y_set_initial : false,
1, 26 1, 27
array_y_set_initial : false, array_y_set_initial : false,
1, 28 1, 29
array_y_set_initial : false, if glob_html_log
1, 30
then html_log_file : openw("html/entry.html"),
omniout_str(ALWAYS, "START of Soultion"), array_x : x_start,
1
array_x : glob_h, glob_next_display : x_start, order_diff : 1, term_no : 1,
2
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(),
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp),
1, 1
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "),
glob_reached_optimal_h : true, glob_optimal_clock_start_sec :
elapsed_time_seconds(), while (glob_current_iter < glob_max_iter)
and not_reached_end(array_x , x_end) and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
1
convfloat(glob_max_sec)) do (if reached_interval
() then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter, atomall(),
if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 1, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1),
ord, term_no
display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"),
if glob_iter >= glob_max_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(),
omniout_str(INFO, "diff ( y , x , 1 ) = x * x ;"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2012-09-21T03:05:28-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "mult"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = x * x ;"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_optimal_expect_sec)), 0)
else (logitem_str(html_log_file, "Done"), 0),
log_revs(html_log_file, " 130 | "), logitem_str(html_log_file, "mult diffeq.max"), logitem_str(html_log_file, "mult maxima results"),
logitem_str(html_log_file, "c c++ Maple and Maxima"), logend(html_log_file)),
if glob_html_log then close(html_log_file))
(%i51) main()
"##############ECHO OF PROBLEM#################"
"##############temp/multpostode.ode#################"
"diff ( y , x , 1 ) = x * x ;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits : 32,"
"max_terms : 30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start : 0.1,"
"x_end : 10.0 ,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_h : 0.00001 ,"
"glob_look_poles : true,"
"glob_max_iter : 20,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_h : 0.005 ,"
"glob_display_interval : 0.1,"
"glob_look_poles : true,"
"glob_max_iter : 10000,"
"glob_max_minutes : 10,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := ("
" (1.0 + x * x * x / 3.0) "
");"
""
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
x[1] = 0.1 " "
y[1] (analytic) = 1.0003333333333333 " "
y[1] (numeric) = 1.0003333333333333 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2000000000000001 " "
y[1] (analytic) = 1.0026666666666666 " "
y[1] (numeric) = 1.0026666666666664 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.214540607629966700000000000000E-14 "%"
Correct digits = 16
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.30000000000000016 " "
y[1] (analytic) = 1.0090000000000001 " "
y[1] (numeric) = 1.0089999999999997 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.401280573340561000000000000000E-14 "%"
Correct digits = 16
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.40000000000000024 " "
y[1] (analytic) = 1.0213333333333334 " "
y[1] (numeric) = 1.0213333333333328 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.52219792534360800000000000000E-14 "%"
Correct digits = 16
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.5000000000000003 " "
y[1] (analytic) = 1.0416666666666667 " "
y[1] (numeric) = 1.0416666666666663 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.26325641456060100000000000000E-14 "%"
Correct digits = 16
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.6000000000000004 " "
y[1] (analytic) = 1.072 " "
y[1] (numeric) = 1.0720000000000003 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.071311613106635300000000000000E-14 "%"
Correct digits = 16
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.7000000000000005 " "
y[1] (analytic) = 1.1143333333333336 " "
y[1] (numeric) = 1.1143333333333334 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.992622838094806300000000000000E-14 "%"
Correct digits = 16
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.8000000000000006 " "
y[1] (analytic) = 1.170666666666667 " "
y[1] (numeric) = 1.170666666666667 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.9000000000000007 " "
y[1] (analytic) = 1.2430000000000005 " "
y[1] (numeric) = 1.2429999999999999 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.35908137389455900000000000000E-14 "%"
Correct digits = 16
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0000000000000007 " "
y[1] (analytic) = 1.333333333333334 " "
y[1] (numeric) = 1.3333333333333337 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.665334536937734300000000000000E-14 "%"
Correct digits = 16
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1049999999999984 " "
y[1] (analytic) = 1.4497442083333314 " "
y[1] (numeric) = 1.4497442083333338 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 1.6847735208291010000000000000E-13 "%"
Correct digits = 15
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.2049999999999963 " "
y[1] (analytic) = 1.5832300416666611 " "
y[1] (numeric) = 1.583230041666667 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 3.646444026525310000000000000E-13 "%"
Correct digits = 15
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.3049999999999942 " "
y[1] (analytic) = 1.7408158749999902 " "
y[1] (numeric) = 1.7408158749999991 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 5.1020813427504520000000000000E-13 "%"
Correct digits = 15
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.404999999999992 " "
y[1] (analytic) = 1.9245017083333176 " "
y[1] (numeric) = 1.9245017083333307 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 6.8072850410314410000000000000E-13 "%"
Correct digits = 15
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.50499999999999 " "
y[1] (analytic) = 2.1362875416666434 " "
y[1] (numeric) = 2.136287541666661 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 8.3151579773498570000000000000E-13 "%"
Correct digits = 15
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.6049999999999878 " "
y[1] (analytic) = 2.3781733749999683 " "
y[1] (numeric) = 2.3781733749999914 " "
absolute error = 2.309263891220325600000000000000E-14 " "
relative error = 9.710241967620870000000000000E-13 "%"
Correct digits = 15
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.7049999999999856 " "
y[1] (analytic) = 2.652159208333291 " "
y[1] (numeric) = 2.6521592083333205 " "
absolute error = 2.93098878501041300000000000000E-14 " "
relative error = 1.1051330462368239000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.8049999999999835 " "
y[1] (analytic) = 2.960245041666613 " "
y[1] (numeric) = 2.960245041666649 " "
absolute error = 3.59712259978550700000000000000E-14 " "
relative error = 1.215143526685998000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.9049999999999814 " "
y[1] (analytic) = 3.3044308749999325 " "
y[1] (numeric) = 3.3044308749999747 " "
absolute error = 4.21884749357559500000000000000E-14 " "
relative error = 1.2767243901192762000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 2.0049999999999795 " "
y[1] (analytic) = 3.686716708333251 " "
y[1] (numeric) = 3.686716708333301 " "
absolute error = 5.018208071305708000000000000000E-14 " "
relative error = 1.3611591202445328000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 2.1049999999999773 " "
y[1] (analytic) = 4.109102541666566 " "
y[1] (numeric) = 4.109102541666625 " "
absolute error = 5.95079541199083900000000000000E-14 " "
relative error = 1.448198323514536000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 2.204999999999975 " "
y[1] (analytic) = 4.573588374999880 " "
y[1] (numeric) = 4.573588374999948 " "
absolute error = 6.92779167366097700000000000000E-14 " "
relative error = 1.514738779626437200000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 2.304999999999973 " "
y[1] (analytic) = 5.08217420833319 " "
y[1] (numeric) = 5.082174208333269 " "
absolute error = 7.90478793533111500000000000000E-14 " "
relative error = 1.5553949178620663000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 2.404999999999971 " "
y[1] (analytic) = 5.636860041666500 " "
y[1] (numeric) = 5.636860041666586 " "
absolute error = 8.70414851306122700000000000000E-14 " "
relative error = 1.544148417509388000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 2.504999999999969 " "
y[1] (analytic) = 6.2396458749998045 " "
y[1] (numeric) = 6.239645874999906 " "
absolute error = 1.01252339845814280000000000000E-13 " "
relative error = 1.6227257423614197000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 2.6049999999999667 " "
y[1] (analytic) = 6.892531708333107 " "
y[1] (numeric) = 6.892531708333222 " "
absolute error = 1.15463194561016280000000000000E-13 " "
relative error = 1.675192794853895000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 2.7049999999999645 " "
y[1] (analytic) = 7.597517541666407 " "
y[1] (numeric) = 7.597517541666536 " "
absolute error = 1.29674049276218280000000000000E-13 " "
relative error = 1.7067949967217336000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 2.8049999999999624 " "
y[1] (analytic) = 8.356603374999704 " "
y[1] (numeric) = 8.35660337499985 " "
absolute error = 1.45661260830820540000000000000E-13 " "
relative error = 1.7430677787890790000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 2.9049999999999603 " "
y[1] (analytic) = 9.171789208333 " "
y[1] (numeric) = 9.171789208333161 " "
absolute error = 1.6164847238542280000000000000E-13 " "
relative error = 1.7624529817863410000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 3.004999999999958 " "
y[1] (analytic) = 10.045075041666289 " "
y[1] (numeric) = 10.045075041666468 " "
absolute error = 1.7941204077942530000000000000E-13 " "
relative error = 1.786069691219192800000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 3.104999999999956 " "
y[1] (analytic) = 10.978460874999577 " "
y[1] (numeric) = 10.978460874999774 " "
absolute error = 1.9717560917342780000000000000E-13 " "
relative error = 1.7960223333531294000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 3.204999999999954 " "
y[1] (analytic) = 11.97394670833286 " "
y[1] (numeric) = 11.973946708333083 " "
absolute error = 2.2204460492503130000000000000E-13 " "
relative error = 1.85439780494853000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 3.3049999999999518 " "
y[1] (analytic) = 13.03353254166614 " "
y[1] (numeric) = 13.033532541666384 " "
absolute error = 2.4336088699783430000000000000E-13 " "
relative error = 1.867190542700899200000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 3.4049999999999496 " "
y[1] (analytic) = 14.159218374999417 " "
y[1] (numeric) = 14.159218374999684 " "
absolute error = 2.66453525910037570000000000000E-13 " "
relative error = 1.8818378165599026000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 3.5049999999999475 " "
y[1] (analytic) = 15.353004208332687 " "
y[1] (numeric) = 15.353004208332983 " "
absolute error = 2.96651592179841800000000000000E-13 " "
relative error = 1.9322055029388788000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 3.6049999999999454 " "
y[1] (analytic) = 16.61689004166596 " "
y[1] (numeric) = 16.616890041666277 " "
absolute error = 3.1619151741324460000000000000E-13 " "
relative error = 1.9028320980665533000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 3.7049999999999432 " "
y[1] (analytic) = 17.952875874999222 " "
y[1] (numeric) = 17.95287587499957 " "
absolute error = 3.4816594052244910000000000000E-13 " "
relative error = 1.939332410843977000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 3.804999999999941 " "
y[1] (analytic) = 19.36296170833248 " "
y[1] (numeric) = 19.362961708332858 " "
absolute error = 3.7658764995285310000000000000E-13 " "
relative error = 1.9448866120041738000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 3.904999999999939 " "
y[1] (analytic) = 20.849147541665737 " "
y[1] (numeric) = 20.849147541666134 " "
absolute error = 3.9790393202565610000000000000E-13 " "
relative error = 1.9084901731855924000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 4.004999999999937 " "
y[1] (analytic) = 22.413433374998988 " "
y[1] (numeric) = 22.413433374999425 " "
absolute error = 4.3698378249246160000000000000E-13 " "
relative error = 1.9496512434364213000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 4.104999999999935 " "
y[1] (analytic) = 24.057819208332234 " "
y[1] (numeric) = 24.057819208332702 " "
absolute error = 4.6895820560166610000000000000E-13 " "
relative error = 1.949296407711161900000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 4.204999999999933 " "
y[1] (analytic) = 25.784305041665476 " "
y[1] (numeric) = 25.784305041665988 " "
absolute error = 5.1159076974727210000000000000E-13 " "
relative error = 1.984116961541450800000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 4.30499999999993 " "
y[1] (analytic) = 27.59489087499871 " "
y[1] (numeric) = 27.594890874999265 " "
absolute error = 5.5422333389287810000000000000E-13 " "
relative error = 2.0084273440450923000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 4.404999999999928 " "
y[1] (analytic) = 29.491576708331944 " "
y[1] (numeric) = 29.49157670833253 " "
absolute error = 5.8619775700208270000000000000E-13 " "
relative error = 1.9876785931098434000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 4.504999999999926 " "
y[1] (analytic) = 31.476362541665168 " "
y[1] (numeric) = 31.476362541665793 " "
absolute error = 6.2527760746888820000000000000E-13 " "
relative error = 1.9864989375478506000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 4.604999999999924 " "
y[1] (analytic) = 33.55124837499839 " "
y[1] (numeric) = 33.55124837499906 " "
absolute error = 6.7501559897209520000000000000E-13 " "
relative error = 2.0118941370750934000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 4.704999999999922 " "
y[1] (analytic) = 35.7182342083316 " "
y[1] (numeric) = 35.71823420833234 " "
absolute error = 7.3896444519050420000000000000E-13 " "
relative error = 2.0688717165590848000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 4.80499999999992 " "
y[1] (analytic) = 37.97932004166481 " "
y[1] (numeric) = 37.97932004166559 " "
absolute error = 7.7449158197850920000000000000E-13 " "
relative error = 2.0392455186898062000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 4.904999999999918 " "
y[1] (analytic) = 40.33650587499802 " "
y[1] (numeric) = 40.336505874998835 " "
absolute error = 8.1712414612411520000000000000E-13 " "
relative error = 2.02576829201906000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 5.0049999999999155 " "
y[1] (analytic) = 42.79179170833122 " "
y[1] (numeric) = 42.7917917083321 " "
absolute error = 8.8107299234252420000000000000E-13 " "
relative error = 2.058976633528028800000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 5.104999999999913 " "
y[1] (analytic) = 45.347177541664415 " "
y[1] (numeric) = 45.34717754166535 " "
absolute error = 9.3791641120333220000000000000E-13 " "
relative error = 2.0683016276847363000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 5.204999999999911 " "
y[1] (analytic) = 48.00466337499759 " "
y[1] (numeric) = 48.0046633749986 " "
absolute error = 1.0089706847793423000000000000E-12 " "
relative error = 2.101818060669596000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 5.304999999999910 " "
y[1] (analytic) = 50.76624920833078 " "
y[1] (numeric) = 50.76624920833183 " "
absolute error = 1.0516032489249483000000000000E-12 " "
relative error = 2.071461384924177800000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 5.404999999999907 " "
y[1] (analytic) = 53.63393504166395 " "
y[1] (numeric) = 53.63393504166506 " "
absolute error = 1.1084466677857563000000000000E-12 " "
relative error = 2.0666890596871026000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 5.504999999999905 " "
y[1] (analytic) = 56.609720874997116 " "
y[1] (numeric) = 56.60972087499829 " "
absolute error = 1.1723955140041653000000000000E-12 " "
relative error = 2.071014475752306000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 5.604999999999903 " "
y[1] (analytic) = 59.69560670833028 " "
y[1] (numeric) = 59.69560670833151 " "
absolute error = 1.2292389328649733000000000000E-12 " "
relative error = 2.05917822206075020000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 5.704999999999900 " "
y[1] (analytic) = 62.89359254166343 " "
y[1] (numeric) = 62.893592541664724 " "
absolute error = 1.2931877790833823000000000000E-12 " "
relative error = 2.0561518698851858000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 5.8049999999998985 " "
y[1] (analytic) = 66.20567837499658 " "
y[1] (numeric) = 66.20567837499793 " "
absolute error = 1.3500311979441904000000000000E-12 " "
relative error = 2.0391471412730766000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 5.904999999999896 " "
y[1] (analytic) = 69.63386420832973 " "
y[1] (numeric) = 69.63386420833113 " "
absolute error = 1.4068746168049984000000000000E-12 " "
relative error = 2.02038854629111000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 6.004999999999894 " "
y[1] (analytic) = 73.18015004166286 " "
y[1] (numeric) = 73.18015004166438 " "
absolute error = 1.5205614545266144000000000000E-12 " "
relative error = 2.077833201573008000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 6.104999999999892 " "
y[1] (analytic) = 76.84653587499598 " "
y[1] (numeric) = 76.8465358749976 " "
absolute error = 1.6200374375330284000000000000E-12 " "
relative error = 2.1081463452930346000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 6.20499999999989 " "
y[1] (analytic) = 80.63502170832909 " "
y[1] (numeric) = 80.6350217083308 " "
absolute error = 1.7053025658242404000000000000E-12 " "
relative error = 2.1148410823185695000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 6.304999999999888 " "
y[1] (analytic) = 84.5476075416622 " "
y[1] (numeric) = 84.54760754166398 " "
absolute error = 1.7763568394002505000000000000E-12 " "
relative error = 2.1010137259353223000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 6.404999999999886 " "
y[1] (analytic) = 88.58629337499531 " "
y[1] (numeric) = 88.58629337499717 " "
absolute error = 1.8616219676914625000000000000E-12 " "
relative error = 2.101478566002323000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 6.5049999999998835 " "
y[1] (analytic) = 92.7530792083284 " "
y[1] (numeric) = 92.75307920833033 " "
absolute error = 1.9326762412674725000000000000E-12 " "
relative error = 2.0836787929450598000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 6.604999999999881 " "
y[1] (analytic) = 97.0499650416615 " "
y[1] (numeric) = 97.0499650416635 " "
absolute error = 2.0037305148434825000000000000E-12 " "
relative error = 2.0646380593576963000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 6.704999999999880 " "
y[1] (analytic) = 101.47895087499457 " "
y[1] (numeric) = 101.47895087499668 " "
absolute error = 2.1174173525650986000000000000E-12 " "
relative error = 2.086558182074044000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 6.804999999999877 " "
y[1] (analytic) = 106.04203670832766 " "
y[1] (numeric) = 106.04203670832986 " "
absolute error = 2.2026824808563106000000000000E-12 " "
relative error = 2.0771785880677357000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 6.904999999999875 " "
y[1] (analytic) = 110.7412225416607 " "
y[1] (numeric) = 110.74122254166302 " "
absolute error = 2.3163693185779266000000000000E-12 " "
relative error = 2.0916956354771246000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 7.004999999999873 " "
y[1] (analytic) = 115.57850837499376 " "
y[1] (numeric) = 115.5785083749962 " "
absolute error = 2.4442670110147446000000000000E-12 " "
relative error = 2.1148110019592356000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 7.104999999999870 " "
y[1] (analytic) = 120.55589420832682 " "
y[1] (numeric) = 120.55589420832935 " "
absolute error = 2.5295321393059567000000000000E-12 " "
relative error = 2.0982235301865823000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 7.204999999999869 " "
y[1] (analytic) = 125.67538004165986 " "
y[1] (numeric) = 125.67538004166248 " "
absolute error = 2.6147972675971687000000000000E-12 " "
relative error = 2.0805962685216428000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 7.3049999999998665 " "
y[1] (analytic) = 130.93896587499287 " "
y[1] (numeric) = 130.9389658749956 " "
absolute error = 2.7284841053187847000000000000E-12 " "
relative error = 2.083783148191091000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 7.404999999999864 " "
y[1] (analytic) = 136.3486517083259 " "
y[1] (numeric) = 136.34865170832873 " "
absolute error = 2.8421709430404010000000000000E-12 " "
relative error = 2.0844877506528717000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 7.504999999999862 " "
y[1] (analytic) = 141.9064375416589 " "
y[1] (numeric) = 141.90643754166186 " "
absolute error = 2.9558577807620170000000000000E-12 " "
relative error = 2.0829624307172656000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 7.60499999999986 " "
y[1] (analytic) = 147.61432337499193 " "
y[1] (numeric) = 147.61432337499497 " "
absolute error = 3.0411229090532290000000000000E-12 " "
relative error = 2.060181450906844000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 7.704999999999858 " "
y[1] (analytic) = 153.4743092083249 " "
y[1] (numeric) = 153.47430920832807 " "
absolute error = 3.154809746774845000000000000E-12 " "
relative error = 2.055594687507294000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 7.804999999999856 " "
y[1] (analytic) = 159.48839504165787 " "
y[1] (numeric) = 159.48839504166116 " "
absolute error = 3.296918293926865000000000000E-12 " "
relative error = 2.0671838180237004000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 7.904999999999854 " "
y[1] (analytic) = 165.65858087499086 " "
y[1] (numeric) = 165.65858087499427 " "
absolute error = 3.410605131648481000000000000E-12 " "
relative error = 2.0588158570682122000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 8.004999999999852 " "
y[1] (analytic) = 171.9868667083238 " "
y[1] (numeric) = 171.98686670832737 " "
absolute error = 3.581135388230905000000000000E-12 " "
relative error = 2.0822144485626506000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 8.104999999999867 " "
y[1] (analytic) = 178.47525254165794 " "
y[1] (numeric) = 178.47525254166047 " "
absolute error = 2.5295321393059567000000000000E-12 " "
relative error = 1.4173013363382345000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 8.204999999999883 " "
y[1] (analytic) = 185.12573837499212 " "
y[1] (numeric) = 185.12573837499357 " "
absolute error = 1.4495071809506044000000000000E-12 " "
relative error = 7.8298522597353350000000000000E-13 "%"
Correct digits = 15
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 8.304999999999898 " "
y[1] (analytic) = 191.94032420832636 " "
y[1] (numeric) = 191.94032420832676 " "
absolute error = 3.9790393202565610000000000000E-13 " "
relative error = 2.0730606435455579000000000000E-13 "%"
Correct digits = 15
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 8.404999999999914 " "
y[1] (analytic) = 198.92101004166057 " "
y[1] (numeric) = 198.92101004166 " "
absolute error = 5.6843418860808010000000000000E-13 " "
relative error = 2.8575874840421905000000000000E-13 "%"
Correct digits = 15
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 8.50499999999993 " "
y[1] (analytic) = 206.06979587499492 " "
y[1] (numeric) = 206.06979587499325 " "
absolute error = 1.6768808563938364000000000000E-12 " "
relative error = 8.1374412454460720000000000000E-13 "%"
Correct digits = 15
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 8.604999999999945 " "
y[1] (analytic) = 213.3886817083293 " "
y[1] (numeric) = 213.3886817083266 " "
absolute error = 2.7000623958883807000000000000E-12 " "
relative error = 1.2653259649351814000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 8.704999999999961 " "
y[1] (analytic) = 220.87966754166374 " "
y[1] (numeric) = 220.8796675416599 " "
absolute error = 3.836930773104541000000000000E-12 " "
relative error = 1.7371136129498177000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 8.804999999999977 " "
y[1] (analytic) = 228.54475337499818 " "
y[1] (numeric) = 228.5447533749933 " "
absolute error = 4.888534022029489300000000000E-12 " "
relative error = 2.1389832625071645000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 8.899999999999991 " "
y[1] (analytic) = 235.989666666666 " "
y[1] (numeric) = 235.98966666665996 " "
absolute error = 6.0538241086760540000000000000E-12 " "
relative error = 2.5652920291747540000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 9.000000000000007 " "
y[1] (analytic) = 244.00000000000057 " "
y[1] (numeric) = 243.99999999999332 " "
absolute error = 7.247535904753022000000000000E-12 " "
relative error = 2.9703016003086086000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 9.100000000000023 " "
y[1] (analytic) = 252.1903333333352 " "
y[1] (numeric) = 252.19033333332663 " "
absolute error = 8.554934538551606000000000000E-12 " "
relative error = 3.3922531547805335000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 9.200000000000038 " "
y[1] (analytic) = 260.56266666666994 " "
y[1] (numeric) = 260.5626666666601 " "
absolute error = 9.833911462919787000000000000E-12 " "
relative error = 3.774106086924577400000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 9.300000000000054 " "
y[1] (analytic) = 269.11900000000463 " "
y[1] (numeric) = 269.1189999999935 " "
absolute error = 1.114131009671837100000000000E-11 " "
relative error = 4.139919551097536000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 9.40000000000007 " "
y[1] (analytic) = 277.8613333333395 " "
y[1] (numeric) = 277.86133333332714 " "
absolute error = 1.23350218927953390000000000E-11 " "
relative error = 4.439272548223718300000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 9.500000000000085 " "
y[1] (analytic) = 286.79166666667436 " "
y[1] (numeric) = 286.7916666666606 " "
absolute error = 1.37561073643155400000000000E-11 " "
relative error = 4.796550584680576700000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 9.600000000000101 " "
y[1] (analytic) = 295.9120000000093 " "
y[1] (numeric) = 295.911999999994 " "
absolute error = 1.529087967355735600000000000E-11 " "
relative error = 5.1673739738695550000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 9.700000000000117 " "
y[1] (analytic) = 305.2243333333443 " "
y[1] (numeric) = 305.2243333333276 " "
absolute error = 1.671196514507755600000000000E-11 " "
relative error = 5.475305642432492000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 9.800000000000132 " "
y[1] (analytic) = 314.7306666666794 " "
y[1] (numeric) = 314.7306666666612 " "
absolute error = 1.818989403545856500000000000E-11 " "
relative error = 5.77951117001346000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 9.900000000000148 " "
y[1] (analytic) = 324.4330000000145 " "
y[1] (numeric) = 324.4329999999948 " "
absolute error = 1.966782292583957300000000000E-11 " "
relative error = 6.062214055240587000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 10.000000000000163 " "
y[1] (analytic) = 334.3333333333497 " "
y[1] (numeric) = 334.3333333333285 " "
absolute error = 2.12025952350813900000000000E-11 " "
relative error = 6.341753310592328000000000000E-12 "%"
Correct digits = 14
h = 5.000E-3 " "
"Finished!"
"diff ( y , x , 1 ) = x * x ;"
Iterations = 1980
"Total Elapsed Time "= 9 Minutes 10 Seconds
"Elapsed Time(since restart) "= 9 Minutes 9 Seconds
"Time to Timeout "= 49 Seconds
Percent Done = 100.05050505050671 "%"
(%o51) true
(%o51) diffeq.max